let x, y, z be set ; :: thesis: ( [<*x,y*>,and2a] in InnerVertices (GFA2CarryStr (x,y,z)) & [<*y,z*>,and2c] in InnerVertices (GFA2CarryStr (x,y,z)) & [<*z,x*>,nor2] in InnerVertices (GFA2CarryStr (x,y,z)) & GFA2CarryOutput (x,y,z) in InnerVertices (GFA2CarryStr (x,y,z)) )
set f1 = and2a ;
set f2 = and2c ;
set f3 = nor2 ;
set xy = [<*x,y*>,and2a];
set yz = [<*y,z*>,and2c];
set zx = [<*z,x*>,nor2];
InnerVertices (GFA2CarryStr (x,y,z)) = {[<*x,y*>,and2a],[<*y,z*>,and2c],[<*z,x*>,nor2]} \/ {(GFA2CarryOutput (x,y,z))} by Th74
.= {[<*x,y*>,and2a],[<*y,z*>,and2c],[<*z,x*>,nor2],(GFA2CarryOutput (x,y,z))} by ENUMSET1:6 ;
hence ( [<*x,y*>,and2a] in InnerVertices (GFA2CarryStr (x,y,z)) & [<*y,z*>,and2c] in InnerVertices (GFA2CarryStr (x,y,z)) & [<*z,x*>,nor2] in InnerVertices (GFA2CarryStr (x,y,z)) & GFA2CarryOutput (x,y,z) in InnerVertices (GFA2CarryStr (x,y,z)) ) by ENUMSET1:def 2; :: thesis: verum